Question

if the 10th term of an AP is 52 and 17th ter. is 20 more than its 13th term , find AP​

Answer 1

Answer:

AP is 7,12,17,22.....

Step-by-step explanation:

Let the first term of the AP be a and common difference be d.

a+(10-1)d = 52

a+ 9d =52

a = 52 - 9d. -equation 1

a+ (17-1)d = a + (13-1)d + 20

a + 16d = a + 12d + 20

16d - 12d = 20

4d = 20

d = 20/4 = 5

a = 52 - 9(5) = 52 - 45 = 7

Therefore, the AP is 7, 12, 17, 22....

PLEASE MARK MY ANSWER AS BRAINLIEST.

Answer 2

Solution :

We know that formula of an A.P;

$\boxed{\bf{a_n=a+(n-1)d}}}$

• a is the first term
• d is the common difference
• n is the term of an A.P.

A/q

$\longrightarrow\sf{a_{10} = 52}\\\\\longrightarrow\sf{a+(10-1)d= 52}\\\\\longrightarrow\sf{a+9d=52...................(1)}$

&

$\longrightarrow\sf{a_{17} = 20+a_{13} }\\\\\longrightarrow\sf{a+(17-1)d= 20 + a+(13-1)d}\\\\\longrightarrow\sf{\cancel{a}+16d = 20 \cancel{+ a} + 12d}\\\\\longrightarrow\sf{16d = 20 + 12d}\\\\\longrightarrow\sf{ 16d - 12d = 20}\\\\\longrightarrow\sf{ 4d = 20}\\\\\longrightarrow\sf{d=\cancel{20/4}}\\\\\longrightarrow\bf{d= 5}$

∴ Putting the value of d in equation (1),we get;

$\longrightarrow\sf{a + 9(5) = 52}\\\\\longrightarrow\sf{a+ 45= 52}\\\\\longrightarrow\sf{a=52 - 45}\\\\\longrightarrow\bf{a = 7}$

$\boxed{\bf{Arithmetic\:Progression\::}}}}$

$\bullet\:\sf{a=\boxed{\bf{7}}}\\\\\bullet\sf{a+d=7+5=\boxed{\bf{12}}}\\\\\bullet\sf{a+2d=7+2(5)=7+10=\boxed{\bf{17}}}\\\\\bullet\sf{a+3d=7+3(5)=7+15=\boxed{\bf{22}}}\\\\\bullet\sf{a+4d=7+4(5)=7+20=\boxed{\bf{27}}}$